{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from manim import *\n",
    "\n",
    "config.progress_bar = \"none\"\n",
    "config.media_width = \"100%\"\n",
    "config.media_embed = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class PolygramScene(Scene):\n",
    "    def construct(self):\n",
    "        self.add(NumberPlane().set_opacity(0.2))\n",
    "        # 传入点集, 自定义多边形\n",
    "        hexagram = Polygram(\n",
    "            [[0, 2, 0], [-np.sqrt(3), -1, 0], [np.sqrt(3), -1, 0]],\n",
    "            [[-np.sqrt(3), 1, 0], [0, -2, 0], [np.sqrt(3), 1, 0]],\n",
    "        ).set_color_by_gradient([WHITE, BLUE])\n",
    "        self.add(hexagram)\n",
    "\n",
    "        dot = Dot()\n",
    "        self.play(MoveAlongPath(dot, hexagram), run_time=5, rate_func=linear)\n",
    "        self.remove(dot)\n",
    "        self.wait()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video controls autoplay loop style=\"max-width: 100%;\"  >\n",
       " <source 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type=\"video/mp4\">\n",
       " Your browser does not support the video tag.\n",
       " </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%manim -v WARNING -qm PolygramScene"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class StarScene(Scene):\n",
    "    def construct(self):\n",
    "        self.add(NumberPlane().set_opacity(0.2))\n",
    "        star = Star().set_color_by_gradient([WHITE, BLUE])\n",
    "        self.add(star)\n",
    "\n",
    "        dot = Dot()\n",
    "        self.play(MoveAlongPath(dot, star), run_time=5, rate_func=linear)\n",
    "        self.remove(dot)\n",
    "        self.wait()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video controls autoplay loop style=\"max-width: 100%;\"  >\n",
       " <source 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type=\"video/mp4\">\n",
       " Your browser does not support the video tag.\n",
       " </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%manim -v WARNING -qm StarScene"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "class PolyStarScene(Scene):\n",
    "    # 自己画的五角星\n",
    "    def construct(self):\n",
    "        self.add(NumberPlane().set_opacity(0.2))\n",
    "        r = 2\n",
    "        angles = [PI / 2 + PI * 4 / 5 - i * PI * 4 / 5 for i in range(5)]\n",
    "        poly_star = Polygram([[r * np.cos(angle), r * np.sin(angle), 0] for angle in angles])\n",
    "        self.add(poly_star)\n",
    "\n",
    "        dot = Dot()\n",
    "        self.play(MoveAlongPath(dot, poly_star), run_time=3, rate_func=rush_into)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video controls autoplay loop style=\"max-width: 100%;\"  >\n",
       " <source 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type=\"video/mp4\">\n",
       " Your browser does not support the video tag.\n",
       " </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%manim -v WARNING -qm PolyStarScene"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "2c0948b606a87f16a1329dbdb4c9bf2c1b73f2116240f6b736465dcfd150b23b"
  },
  "kernelspec": {
   "display_name": "Python 3.8.12 ('manim')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.12"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
